Mellin amplitudes for dual conformal integrals

  • Miguel F. Paulos
  • Marcus Spradlin
  • Anastasia Volovich
Open Access


Motivated by recent work on the utility of Mellin space for representing conformal correlators in AdS/CFT, we study its suitability for representing dual conformal integrals of the type which appear in perturbative scattering amplitudes in super-Yang-Mills theory. We discuss Feynman-like rules for writing Mellin amplitudes for a large class of integrals in any dimension, and find explicit representations for several familiar toy integrals. However we show that the power of Mellin space is that it provides simple representations even for fully massive integrals, which except for the single case of the 4-mass box have not yet been computed by any available technology. Mellin space is also useful for exhibiting differential relations between various multi-loop integrals, and we show that certain higher-loop integrals may be written as integral operators acting on the fully massive scalar n-gon in n dimensions, whose Mellin amplitude is exactly 1. Our chief example is a very simple formula expressing the 6-mass double box as a single integral of the 6-mass scalar hexagon in 6 dimensions.


Scattering Amplitudes Conformal and W Symmetry Duality in Gauge Field Theories AdS-CFT Correspondence 


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Copyright information

© SISSA 2012

Authors and Affiliations

  • Miguel F. Paulos
    • 1
  • Marcus Spradlin
    • 2
  • Anastasia Volovich
    • 2
  1. 1.Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589Université Pierre et Marie CurieParis Cedex 05France
  2. 2.Department of PhysicsBrown UniversityProvidenceU.S.A.

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